Comparison To Efforts By Individuals
As of the end of 2007, thanks to the constant decline in memory prices, the ready availability of multi-core 64-bit computers, and the availability of the efficient sieving code (developed by Thorsten Kleinjung of the Bonn group) via ggnfs and of robust open-source software such as msieve for the finishing stages, special-form numbers of up to 750 bits and general-form numbers of up to about 520 bits can be factored in a few months on a few PCs by a single person without any special mathematical experience. These bounds increase to about 950 and 600 if it were possible to secure the collaboration of a few dozen PCs for sieving; currently the amount of memory and the CPU power of a single machine for the finishing stage are equal barriers to progress.
In 2009, Benjamin Moody factored a 512-bit RSA key used to sign the TI-83 graphing calculator using software found on the internet; this eventually led to the Texas Instruments signing key controversy.
Read more about this topic: Integer Factorization Records
Famous quotes containing the words comparison to, comparison, efforts and/or individuals:
“It is very important not to become hard. The artist must always have one skin too few in comparison to other people, so you feel the slightest wind.”
—Shusha Guppy (b. 1938)
“We teach boys to be such men as we are. We do not teach them to aspire to be all they can. We do not give them a training as if we believed in their noble nature. We scarce educate their bodies. We do not train the eye and the hand. We exercise their understandings to the apprehension and comparison of some facts, to a skill in numbers, in words; we aim to make accountants, attorneys, engineers; but not to make able, earnest, great- hearted men.”
—Ralph Waldo Emerson (1803–1882)
“There is a totalitarian regime inside every one of us. We are ruled by a ruthless politburo which sets ours norms and drives us from one five-year plan to another. The autonomous individual who has to justify his existence by his own efforts is in eternal bondage to himself.”
—Eric Hoffer (1902–1983)
“The people needed to be rehoused, but I feel disgusted and depressed when I see how they have done it. It did not suit the planners to think how they might deal with the community, or the individuals that made up the community. All they could think was, “Sweep it away!” The bureaucrats put their heads together, and if anyone had told them, “A community is people,” they would not have known what they were on about.”
—May Hobbs (b. 1938)